Initialize Cosine Quarter-Wave Transform and Synthesis

Calling Sequence

CALL COSQI	(N, RWSAVE)
CALL DCOSQI	(N, DWSAVE)
CALL VCOSQI	(N, RWSAVE)
CALL VDCOSQI	(N, DWSAVE)
void cosqi	(int n, float *rwsave)
void dcosqi	(int n, double *dwsave)
void vcosqi	(int n, float *rwsave)
void vdcosqi	(int n, double *dwsave)

Arguments

N

Length of the sequence to be transformed. The method is most efficient when N is a product of small primes.

xWSAVE

On entry, an array with a dimension of at least (3 × N + 15) for scalar subroutines or (2 × N + 15) for vector subroutines. The same work array can be used for both xCOSQF and xCOSQB as long as N remains unchanged. Different xWSAVE arrays are required for different values of N. This initialization does not have to be repeated between calls to xCOSQF or xCOSQB as long as N and xWSAVE remain unchanged, thus subsequent transforms can be obtained faster than the first.

Sample Program

PROGRAM TEST

IMPLICIT NONE

C

INTEGER N

PARAMETER (N = 6)

C

INTEGER I

REAL PI, WSAVE(3 * N + 15), X(N)

C

EXTERNAL COSQB, COSQF, COSQI

INTRINSIC ACOS, COS

C

C Initialize array X to a real even quarter-wave sequence,

C that is, it can be expanded in terms of a cosine series

C with only odd wave numbers.

C

PI = ACOS (-1.0)

DO 100, I=1, N

X(I) = COS((I - 1) * PI / (2.0 * N))

100 CONTINUE

C

CALL COSQI (N, WSAVE)

PRINT 1000

PRINT 1010, (X(I), I = 1, N)

CALL COSQF (N, X, WSAVE)

PRINT 1020

PRINT 1010, (X(I), I = 1, N)

CALL COSQB (N, X, WSAVE)

PRINT 1030

PRINT 1010, (X(I), I = 1, N)

C

1000 FORMAT(1X, 'Original Sequence: ')

1010 FORMAT(1X, 100(F7.3, 1X))

1020 FORMAT(1X, 'Transformed Sequence: ')

1030 FORMAT(1X, 'Recovered Sequence: ')

END

Sample Output

Original Sequence:
1.000 0.966 0.866 0.707 0.500 0.259
Transformed Sequence:
6.000 0.000 0.000 0.000 0.000 0.000
Recovered Sequence:
24.000 23.182 20.785 16.971 12.000 6.212